BME
Lecture10 axial stress.pdf

# Lecture10 axial stress.pdf - Deformable Bodies-Axial...

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Deformable Bodies Deformation: The changes in a body’s shape or size. Can be due to an applied force. Can be due to temperature change - thermal expansion or contraction of a roof caused by weather. Deformations can be large or small: Rubber bands undergo large deformations Structural members in a building undergo small deformations when occupied with people vs. when it is empty Deformed body Undeformed body
RIGID BODIES DEFORMABLE BODIES Distance between points in a body is constant. Distance between points in a body is NOT constant. F F F F F F F F F F F F F F F F

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RIGID BODIES DEFORMABLE BODIES Elephant on a bowling ball. Elephant on a beach ball. Same free body diagrams, but are the results the same? In terms of statics - yes. In terms of behavior - no.
Deformable bodies Golf ball hitting a steel plate at 150 mph

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Deformable bodies Golf club hi=ng golf ball. What does this tell us? In the real world, nothing is truly a “rigid body”
Deformable bodies Points can move relaFve to other parts A point’s angular posiFon relaFve to its CM changes This change is a characterisFc feature of a deformable body CM P 1 P’ 1 θ P 1 P’ 1

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RIGID BODIES DEFORMABLE BODIES 1. Have equilibrium equaFons defined by staFcs. 2. Forces have no effect on a body in equilibrium (realisFc only for small forces or very hard objects T diamonds). 3. Internal forces can be determined by staFcs T equilibrium equaFons 1. Have equilibrium equaFons defined by staFcs. 2. Forces cause deformaFons on a body in equilibrium (such as biological materials). 3. Internal forces can be determined by staFcs equilibrium equaFons and/ or deformaFons
RIGID BODIES DEFORMABLE BODIES 1. All bodies are treated the same T infinite sFffness. 2. Since all bodies are treated the same, cannot determine failure due to deformaFons 1. The ability, amount and method of deformaFon is a characterisFc of each Fssue/ material. 2. The characterisFcs of deformaFon dictates the ability of biological materials and their replacements to funcFon mechanically

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STATICS DEFORMATIONS 1. Gives informaFon about forces. 2. When applied forces are known, can predict internal forces 3. When not enough forces are known, problems are staFcally indeterminant. 1. Gives informaFon about material properFes. 2. When applied forces are known, can predict deformaFons. 3. DeformaFons can be used to determine forces. StaFcs only gives half the story T combining staFcs with deformaFons allows us to characterize materials and devices.
Why is it important to characterize materials and devices? Deformable bodies Wood Fiberglass and carbon fiber

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Characterizing Materials For the pole vaulter’s pole We want something that won’t break Flexible Stiff Light Elastic - will return stored energy and lift person higher For the general case Knowing material properties like spring constants, elastic moduli, maximum stresses: Gives information on material performance under a load.
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• Fall '17
• Force, ........., ε

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